Berg, PeterBuono, Pietro-LucianoMizanski, John S.2013-07-082022-03-292013-07-082022-03-292013-05-01https://hdl.handle.net/10155/317Presented in this thesis is a macro-economic model based on a three-factor production function, utilizing energy, capital, and labour as the three production factors. With a primary focus on energy production we include two sources of energy, the rst derived from a xed amount of natural resources and the other generated from renewable sources. The production of energy from non-renewable sources is based on a Hubbert-type model of extraction. The production of energy from renewables is dependent on investment, innovation, and a natural limit to energy production. We also seek to include an aspect of investment in technology through the inclusion of e ciency and innovation factors. Two models of growth are examined for e ciency and innovation. The model, a set of di erential algebraic equations, has been implemented in a C++ program which is provided at the end of this thesis. We provide two solution methods, the rst based on a classic Runge-Kutta fourth order solution combined with Newton's method, and the second an implementation of the DASSL implicit DAE solver package. The model shows a promising incremental improvement over the model proposed by Berg et al. [2], however the sheer volume of parameters and the extensive sensitivity of the model to certain parameters introduces new di culties in estimating values and hence the con fidence in long term predictions made.enEnergy productionNatural resourcesRenewable resourcesHubbert-type modelNon-renewable resourcesRunge-Kutta fourth order solutionDASSLDAE solver packageThesis